A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families

Handle URI:
http://hdl.handle.net/10754/552394
Title:
A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families
Authors:
Dutta, Subhajit; Genton, Marc G. ( 0000-0001-6467-2998 )
Abstract:
Several fascinating examples of non-Gaussian bivariate distributions which have marginal distribution functions to be Gaussian have been proposed in the literature. These examples often clarify several properties associated with the normal distribution. In this paper, we generalize this result in the sense that we construct a pp-dimensional distribution for which any proper subset of its components has the Gaussian distribution. However, the jointpp-dimensional distribution is inconsistent with the distribution of these subsets because it is not Gaussian. We study the probabilistic properties of this non-Gaussian multivariate distribution in detail. Interestingly, several popular tests of multivariate normality fail to identify this pp-dimensional distribution as non-Gaussian. We further extend our construction to a class of elliptically contoured distributions as well as skewed distributions arising from selections, for instance the multivariate skew-normal distribution.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families 2014, 132:82 Journal of Multivariate Analysis
Journal:
Journal of Multivariate Analysis
Issue Date:
28-Jul-2014
DOI:
10.1016/j.jmva.2014.07.007
Type:
Article
ISSN:
0047259X
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S0047259X1400164X
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorDutta, Subhajiten
dc.contributor.authorGenton, Marc G.en
dc.date.accessioned2015-05-06T13:33:22Zen
dc.date.available2015-05-06T13:33:22Zen
dc.date.issued2014-07-28en
dc.identifier.citationA non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families 2014, 132:82 Journal of Multivariate Analysisen
dc.identifier.issn0047259Xen
dc.identifier.doi10.1016/j.jmva.2014.07.007en
dc.identifier.urihttp://hdl.handle.net/10754/552394en
dc.description.abstractSeveral fascinating examples of non-Gaussian bivariate distributions which have marginal distribution functions to be Gaussian have been proposed in the literature. These examples often clarify several properties associated with the normal distribution. In this paper, we generalize this result in the sense that we construct a pp-dimensional distribution for which any proper subset of its components has the Gaussian distribution. However, the jointpp-dimensional distribution is inconsistent with the distribution of these subsets because it is not Gaussian. We study the probabilistic properties of this non-Gaussian multivariate distribution in detail. Interestingly, several popular tests of multivariate normality fail to identify this pp-dimensional distribution as non-Gaussian. We further extend our construction to a class of elliptically contoured distributions as well as skewed distributions arising from selections, for instance the multivariate skew-normal distribution.en
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0047259X1400164Xen
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Multivariate Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Multivariate Analysis, 28 July 2014. DOI: 10.1016/j.jmva.2014.07.007en
dc.subjectDistribution of products of random variablesen
dc.subjectHalf-normal distributionen
dc.subjectSign functionen
dc.subjectSkewed distributionsen
dc.subjectSymmetric distributionsen
dc.titleA non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related familiesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalJournal of Multivariate Analysisen
dc.eprint.versionPost-printen
kaust.authorDutta, Subhajiten
kaust.authorGenton, Marc G.en
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